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Efficient Broadcasting and Gathering in Wireless Ad-Hoc Networks

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### Efficient Broadcasting and Gathering in Wireless Ad-Hoc Networks

Melih Onus (ASU)

Kishore Kothapalli (JHU)

Andrea Richa (ASU)

Christian Scheideler (JHU)

2005 International Symposium on Parallel Architectures, Algorithms and Networks, Las Vegas Nevada

Mobile devices communicating via radio

Network without centralized control

Broadcasting: Sending a packet from a source node to all nodes in the network

Gathering: Sending one packet from a subset of nodes to a single sink node in the network

Ad-Hoc NetworksOur Results

- Near optimal algorithms for broadcasting and information gathering (time and work)
- A realistic wireless communication model which takes into account
- Different transmission & interference ranges
- Non-uniformity of signal propagation of real antennas
- Physical carrier sensing

v

w

Communication ModelsUnit Disk Graph (UDG) Disk shaped transmission area

v

w

u

R

Packet Radio Network (PRN) Transmission Range = Interference Range

v

ri

rt

w

Communication model- Transmission range, interference area via cost function c

Cost Function:

c(u,v) [(1- )d(u,v), (1+ )d(u,v)]

d(u,v) is Euclidean distance

[0,1),depends on the environment

- For a given transmission range rt, transmission area of v is

{ uV | c(v,u) rt}

- For given interference range ri, interference area of v is

{ uV | c(v,u) ri}

v

ri

rt

w

Communication model (cont.)rt: Transmission range

ri: Interference range

- If c(v,w) ≤ ri, node w can cause interference at node v.

- If c(v,u) ≤rt then v is guaranteed to receive the message from u provided no other node w with c(v, w) ≤ ri also transmits at the same time.

rsi(T)

u

v

Physical Carrier Sensing

rst(T): Carrier sense

transmission (CST) range

rst(T)

rsi(T): Carrier sense

interference (CSI) range

- These ranges grow monotonically in both the sensing threshold T and the transmission power.

14

Constant density spanner

Active node

Inactive node

Gateway node

Gateway edge

Other edges

- Constant density spanner: Given a graph G find a sparse subgraph G’ of G such that distance between any two nodes in G’ is less than a constant factor of original distance.

Constant density spanner (cont.)

Active node

Inactive node

Gateway node

Gateway edge

Other edges

- Active nodes form a maximal independent set
- Gateway nodes connect active nodes which are within 2 or 3 hops from each other

Motivation

- Previously proposed broadcasting and gathering algorithms will not work for the communication model that we have considered.

Isolated Broadcasting

Active node

Inactive node

s

u

Gateway node

v

((( )))

(( ))

( )

Gateway edge

Other edges

- Firstly, node s sends out the broadcast message.

Isolated Broadcasting (cont.)

- If u is a gateway node and has already received the message, it sends out an RTS signal with probability p.

s

u

v

CTS

message

RTS

- If v is an active node or a gateway node and v has not received the broadcast message yet, then v checks if it correctly received an RTS signal. If so, v sends out a CTS signal.

- If v is a gateway node and sent out a RTS signal, then v checks if it received a CTS signal. If so, v sends out the broadcast message.

Isolated Broadcasting (cont.)

Active node

- If node v:
- is an active node
- received the broadcast message in the previous round
- it is the first time it received the broadcast message
- Then, it sends out the broadcast message.

Inactive node

s

u

Gateway node

v

((( )))

(( ))

( )

Gateway edge

Other edges

Our Results

- D(s): diameter with respect to s
- W(s): minimum work for broadcast
- The broadcast algorithm needs O(D(s)+log n) rounds, with high probability, to deliver the broadcast messages to all nodes.
- The broadcast algorithm needs O(W(s)) work
- Extendable to multiple broadcasts

Information Gathering

- Stage I: Building Gathering Tree T(s)
- Stage II: Gathering on Tree T(s)

Building Gathering Tree T(s)

- We select a shortest path tree rooted at s on the spanner graph by running a modified Bellman-Ford type algorithm that takes into account message interference.

- In order to show that this RTS/CTS scheme works efficiently, it is crucial to note that the spanner is of constant density: Hence a constant number of RTS/CTS handshakes are enough to guarantee the successful delivery of a message w.h.p..

Building Gathering Tree T(s) (cont.)

Firstly, node s sends out the route message.

s

u

v

((( )))

(( ))

( )

CTS

<1>

<0>

route m.

RTS

<2>

- If the shortest path estimate d\'(s,u) is not infinite and u needs to broadcast the latest update on d’(s,u), then u sends a RTS signal with probability p

- If v received an RTS signal then v sends a CTS signal.

- If u received a CTS signal, u sends out the route message.

Building Gathering Tree T(s) (cont.)

<6>

<7>

<4>

<5>

s

u

<3>

v

<1>

<6>

<0>

<5>

<2>

<4>

<3>

- Each node u has a label which is the shortest path distance to sink node.

- Each node u has a parent node which is the node that node u received the route message

Gathering on Tree T(s) (Inactive Nodes)

Active node

Inactive node

s

Gateway node

v

Gateway edge

Other edges

I-RTS

w

Inactive nodes have a state {asleep, awake}

If w is inactive and has a packet to send and w is awake then w sends a I-RTS signal to its parent with a probability 1/2.

Gathering on Tree T(s) (Inactive Nodes)

Active node

Inactive node

s

Gateway node

v

Gateway edge

Other edges

I-RTS

w

- If v is active;
- v receives an I-RTS signal, send an I-CTS signal
- v senses a busy channel, send a collision message
- v senses a free channel, send a free message

Gathering on Tree T(s) (Inactive Nodes)

Active node

Inactive node

s

Gateway node

v

Gateway edge

Other edges

w

- If w is inactive;
- w receives an I-CTS signal, send the packet
- w receives a collisionmessage, become asleep with p=1/2
- w receives a free message, become awake

Gathering on Tree T(s) (Active Nodes)

Active node

Inactive node

s

u

Gateway node

v

Gateway edge

message

Other edges

If v is active and has a message to send, then v sends the message to its parent.

Gathering on Tree T(s) (Gateway Nodes)

Active node

Inactive node

s

u

message

RTS

Gateway node

v

Gateway edge

CTS

Other edges

- If u is a gateway node and has a non-empty queue then u sends an RTS message containing the id of its parent with probability p.

- If an active node receives an RTS message containing its id, it sends a CTS message.

- If u receives a CTS message from its parent, then u sends the message to its parent.

Our Results

- : maximum density of inactive nodes
- m: number of messages
- W’(s): the optimal work
- A gathering tree T(s) with sink node s, the information gathering algorithm presented above needs O(m+(logn)(log)+D(s)+logn) time steps w.h.p..
- Once a stable gathering tree has been constructed, the gathering protocol described above needs O(W’(s)) work

Conclusions and Future work

- Algorithms for broadcasting and information gathering on a realistic model for wireless communication
- Node mobility and node faults
- Anycasting and multicasting

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